Counter-Propagating Waves in the Fermi-Pasta-Ulam Model

Wednesday, December 5, 2012 - 9:00am - 9:50am
Keller 3-180
C. Eugene Wayne (Boston University)
We study the interaction of small amplitude, long wavelength solitary
waves in the Fermi-Pasta-Ulam model with general nearest-neighbor
interaction potential. We establish global-in-time existence and
stability of counter-propagating solitary wave solutions. These
solutions are close to the linear superposition
of two solitary waves for large positive and negative values of
time; for intermediate values of time these
solutions describe the interaction of two counter-propagating
pulses. These solutions are stable with respect
to perturbations in the space of square integrable sequences
and asymptotically stable with respect to
perturbations which decay exponentially at spatial infinity.
This is joint work with Aaron Hoffman from Olin College